Question: Solve for $x$ and $y$ using elimination. ${4x+2y = 26}$ ${3x-2y = 2}$
We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $2y$ and $-2y$ cancel out. $7x = 28$ $\dfrac{7x}{{7}} = \dfrac{28}{{7}}$ ${x = 4}$ Now that you know ${x = 4}$ , plug it back into $\thinspace {4x+2y = 26}\thinspace$ to find $y$ ${4}{(4)}{ + 2y = 26}$ $16+2y = 26$ $16{-16} + 2y = 26{-16}$ $2y = 10$ $\dfrac{2y}{{2}} = \dfrac{10}{{2}}$ ${y = 5}$ You can also plug ${x = 4}$ into $\thinspace {3x-2y = 2}\thinspace$ and get the same answer for $y$ : ${3}{(4)}{ - 2y = 2}$ ${y = 5}$